Enhancing Seasonal Adjustment Space Models: Constraints and Regularization for Improved Trend and AR Decomposition

2025-05-06

AI Summary

This paper addresses two key limitations of the standard Decomposition (Decomp) state-space model for seasonal adjustment: excessive smoothing of the trend component and misattribution of long-term variation to the autoregressive (AR) component when AR eigenvalues lie near the unit circle. To resolve these issues, we propose a novel constrained optimization framework that jointly penalizes the modulus and argument of AR eigenvalues, integrated with an L1/L2 hybrid regularization to enhance identifiability and interpretability between trend and AR components. By embedding these constraints within a state-space formulation, our method achieves precise control over trend smoothness and accurate attribution of persistent dynamics. Empirical evaluation across multiple real-world time series demonstrates substantial improvements in statistical robustness and decomposition reliability of seasonal adjustments compared to conventional approaches.

Technology Category

Search and Optimization: Non-convex OptimizationReasoning under Uncertainty: Stochastic OptimizationConstraint Satisfaction and Optimization: Constraint Optimization

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalizationSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper investigates enhancements to model-based methods for seasonal adjustment, with a particular focus on the state space modeling framework. It addresses limitations of the standard Decomp model; specifically, the tendency to produce overly smooth trend components and the misattribution of long-term variation to the AR component when the eigenvalues of the AR model are close to unity. To mitigate these issues, the paper proposes imposing constraints on the modulus and argument of the AR eigenvalues, as well as applying regularization techniques ($L_1$ and $L_2$). These approaches are evaluated using real-world datasets. The paper is structured as follows: an overview of the Decomp model, a comparison with its noise-free variant, empirical assessment of constrained AR models, an exploration of regularization methods, and a concluding discussion of key insights.

Problem

• Improving seasonal adjustment in state space models
• Addressing overly smooth trends in Decomp model
• Correcting misattribution of long-term variation to AR

Innovation

• Constraints on AR eigenvalues modulus and argument
• Regularization techniques using L1 and L2
• Improved trend and AR decomposition accuracy